Method and apparatus for determining error diffusion coefficients

ABSTRACT

Provided are a method and apparatus for determining error diffusion coefficients. The method includes: (a) setting N groups of error diffusion coefficients (N is a positive integer), in which each group includes a plurality of coefficients; (b) binarizing an image having one gray level value using each of the N groups of error diffusion coefficients; (c) detecting N fit values with respect to N binary-coded images using an evaluation function; (d) determining whether the fit values are detected a predetermined number of times; (e) when a detection number of the fit values does not coincide with the predetermined number of times, reproducing the N groups of error diffusion coefficients according to reproduction rates determined by the N fit values; (f) selecting optional error diffusion coefficients in the reproduced N groups of error diffusion coefficients, and substituting portions of data of selected error diffusion coefficients with each other; and (g) determining the N groups of error diffusion coefficients including the error diffusion coefficients containing substituted data as new error diffusion coefficients, and returning to step (b).

PRIORITY

This application claims the benefit under 35 U.S.C. §119(a) of KoreanPatent Application No. 2003-46321, filed on Jul. 9, 2003, in the KoreanIntellectual Property Office, the entire disclosure of which isincorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to error diffusion coefficients used in aprinter which prints an image after binary coding the image. Moreparticularly, the present invention relates to a method and an apparatusfor determining optimal error diffusion coefficients.

2. Description of the Related Art

In general, an image having 256 brightness levels between 0 (black) and255 (white) is referred to as a continual gray level image. A printercan reproduce only two gray levels by either printing a dot or notprinting a dot on a printing medium. Therefore, in order to print animage having 256 gray levels based on a monitor using a printer, a unitfor converting the image into binary codes is needed. A halftone methodis a method of representing a continual gray level image with 0 and 255,and a binary image is an image generated by the halftone method.

An error diffusion method is widely used as the halftone method. Inerror diffusion methods, an input gray level image is converted intobinary code values using a threshold value and errors generated bybinarization are diffused into neighboring pixels. Such error diffusionmethods include the Floyd-Steinberg method, which uses a fixed errordiffusion coefficient, and a method that uses an error diffusioncoefficient that varies with input gray value.

The Floyd-Steinberg method includes adding a gray value of an inputpixel to an error caused by an error diffusion coefficient propagatedusing an error coefficient from neighboring pixels, converting the sumof the input grey value and the error (hereinafter referred to as“combined value”) into a binary code using a threshold value, andfinally transmitting the error to neighboring pixels through an errordiffusion filter having the error diffusion coefficient. In theFloyd-Steinberg method, the combined value is compared with thethreshold value, a binary image of gray level 255 is output when thecombined value is larger than the threshold value, and a binary image ofgray level 0 is output when the combined value is smaller than thethreshold value. After outputting the binary image, an error between thegray level (0 or 255) of the binary image and the combined value iscalculated, and the error is transmitted to peripheral areas, which arenot changed into binary.

The method that uses a changing error diffusion coefficient includesselecting an error diffusion filter from a look-up table, adding theinput gray level value to the error transmitted from neighboring pixels,converting the sum of the input grey value and the error (hereinafterreferred to as a “combined value”) into a binary value using a thresholdvalue, and transmitting the error to neighboring pixels through theerror diffusion filter. In this method, a binary image is output bycomparing the combined value with the threshold value, and the errorbetween the gray level value of the output binary image and the combinedvalue is calculated and transmitted to peripheral portions through theerror diffusion filter.

However, when an image is binarized using a fixed error diffusioncoefficient, a worm artifact is generated, and the image quality islowered since minor pixels are not distributed evenly. Also, when animage is binarized using a changing error diffusion coefficient, theerror diffusion coefficient is determined through trial and erroroperations, and thus, an effective error diffusion coefficient cannot bedetermined in a short time period.

SUMMARY OF THE INVENTION

The present invention provides a method of determining optimal errordiffusion coefficients using a genetic algorithm.

The present invention also provides an apparatus for determining optimalerror diffusion coefficients, which performs the above error diffusioncoefficient determining method.

According to an aspect of the present invention, there is provided amethod of determining error diffusion coefficients, which is used in aprinter that binarizes and prints an image. The method includes settingN groups of error diffusion coefficients (N is a positive integer), inwhich each group includes a plurality of coefficients; binarizing animage having one gray level value using each of the N groups of errordiffusion coefficients; detecting N fit values with respect to Nbinary-coded images using an evaluation function; determining whetherthe fit values are detected a predetermined number of times; when adetection number of the fit values does not coincide with thepredetermined number of times, reproducing the N groups of errordiffusion coefficients according to reproduction rates determined by theN fit values; selecting optional error diffusion coefficients in thereproduced N groups of error diffusion coefficients, and switchingportions of data of selected error diffusion coefficients with eachother; and determining the N groups of error diffusion coefficientsincluding the error diffusion coefficients containing switched data asnew error diffusion coefficients, and returning to the binarizing step.

According to another aspect of the present invention, there is providedan apparatus for determining error diffusion coefficients, which is usedin a printer that binarizes and prints an image. The apparatus includesa coefficient setting unit that sets N groups of error diffusioncoefficients (N is a positive integer), each group including a pluralityof coefficients; an image binarizing unit that binarizes an image havingone gray level value using each of the N groups of error diffusioncoefficients; a fit value detector that detects N fit values withrespect to each of the N binary-coded images using an evaluationfunction; a detection number checking unit that checks whether the fitvalues are detected for a predetermined number of times; a coefficientreproducing unit that reproduces the N groups of error diffusioncoefficients according to reproduction rates determined by the detectedN fit values; a coefficient switching unit that selects optional errordiffusion coefficients in the reproduced N groups of error diffusioncoefficients, and switches portions of data of selected error diffusioncoefficients; and a coefficient determining unit that determines the Ngroups of error diffusion coefficients including the substituted errordiffusion coefficients as new error diffusion coefficients, and outputsthe result of the determination to the image binarizing unit.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features and advantages of the present inventionwill become more apparent by describing in detail exemplary embodimentsthereof with reference to the attached drawings in which:

FIG. 1 is a flowchart illustrating a method of determining errordiffusion coefficients according to an embodiment of the presentinvention;

FIG. 2 illustrates an example of error diffusion coefficients diffusedin a predetermined pixel;

FIG. 3 is a flowchart illustrating Step 10 of the method of FIG. 1according to an embodiment of the present invention;

FIG. 4 illustrates examples of N groups of binary error diffusioncoefficients;

FIG. 5 illustrates an example in which binary error diffusioncoefficients are decoded into decimal-form error diffusion coefficients;

FIG. 6 illustrates an optimal energy spectrum having an ideal blue noisecharacteristic;

FIG. 7 illustrates an example in which portions of the data of selectederror diffusion coefficients of two different groups are switched witheach other;

FIG. 8 illustrates an example of changing a portion of the data of aselected error diffusion coefficient;

FIG. 9 illustrates energy spectra with respect to a binarized imagehaving a gray level of 195;

FIG. 10 illustrates energy spectra with respect to a binarized imagehaving a gray level of 225;

FIG. 11 illustrates energy spectra with respect to a binarized imagehaving a gray level of 250;

FIG. 12 is a block diagram illustrating an apparatus for determiningerror diffusion coefficients according to an embodiment of the presentinvention; and

FIG. 13 is a block diagram illustrating a coefficient setting unit ofthe apparatus shown in FIG. 12.

Throughout the drawings, it should be appreciated that like referencenumbers are used to depict like features and structures.

DETAILED DESCRIPTION OF THE INVENTION

A method of determining error diffusion coefficients according tocertain exemplary embodiments of the present invention will now bedescribed with reference to the accompanying drawings.

FIG. 1 is a flowchart illustrating a method of determining errordiffusion coefficients according to an embodiment of the presentinvention. The method includes reproducing, substituting, and changingerror diffusion coefficients of a group N (steps 10 through 24).

A positive integer number of N groups of error diffusion coefficientsare set, each group containing a plurality of coefficients (step 10).FIG. 2 shows two examples of error diffusion coefficients diffused in apredetermined pixel. FIG. 2( a) shows two error diffusion coefficients(E1 and E2) diffused on a predetermined pixel P1, and FIG. 2( b) showsthree error diffusion coefficients (E1, E2, and E3) diffused in thepredetermined pixel P1. As shown in FIG. 2, two, three, or more errordiffusion coefficients form one group. N groups of error diffusioncoefficients are set. It is desirable that a large number of groups areset, such as a number on the order of hundreds of groups.

FIG. 3 is a flowchart illustrating an example 10A of step 10 shown inFIG. 1. Step 10A includes decoding the binary error diffusioncoefficients into decimal error diffusion coefficients (steps 30 and32).

First, N groups of binary error diffusion coefficients are generated(step 30). FIG. 4 shows an example of N groups of binary error diffusioncoefficients in which each group includes two error diffusioncoefficients generated at an initial stage. In alternative embodiments,each group may include three or more error diffusion coefficients.

After step 30, the N groups of error diffusion coefficients are decodedinto decimal error diffusion coefficients (step 32). FIG. 5 shows anexample of decoding the N groups of binary error diffusion coefficientsshown in FIG. 4 into N groups of decimal error diffusion coefficients.

After step 10, an image having a single gray level value is binary codedusing each of the N groups of error diffusion coefficients (step 12).The single grey level image is an image of predetermined size formed byone predetermined gray level value from 0 through 255. Since there are Ngroups of error diffusion coefficients, the image is binary coded Ntimes. Therefore, N binary-coded images are output. The binary coding isperformed by adding the gray level value of the image to errors obtainedfrom the error diffusion coefficients, and comparing the resultingvalues to a threshold value. Meanwhile, after performing a step 24,which will be described later, the single grey level image is binarycoded using N newly determined groups of error diffusion coefficients.

After step 12, N fit values are determined using an evaluation functionfor each of the N binary-coded images (step 14). The evaluation functionmeans a correlation coefficient between an optimal energy spectrumhaving an ideal blue noise characteristic and energy spectrums of the Nbinary-coded images.

FIG. 6 shows an optimal energy spectrum having an ideal blue noisecharacteristic. The following Equation (1) is a Gaussian function forobtaining the optimal energy spectrum:

$\begin{matrix}\begin{matrix}{{\Pr\left( f_{r} \right)} = {\exp\left( \frac{- \left( {f_{r} - f_{p}} \right)^{2}}{2\;\alpha^{2}} \right)}} & \; & {f_{r} \leq \left( {f_{p} + \alpha} \right)} \\{{\Pr\left( f_{r} \right)} = 0.5} & \; & {{f_{r} > \left( {f_{p} + \alpha} \right)},{\alpha = \left( {f_{p}/10} \right)}}\end{matrix} & (1)\end{matrix}$Here, Pr(ƒ_(r)) denotes energy.

Blue noise is noise with a frequency distribution corresponding to ahigh-pass filter having a high response at a certain frequency definedas a principal frequency. An ideal principal frequency fp is defined byEquation 2 below with respect to an image of a predetermined size thathas a single grey level value x:

$\begin{matrix}{f_{p} = \left\{ \begin{matrix}\sqrt{1 - {x/255}} & {x \geq 128} \\\sqrt{x/255} & {x < 128}\end{matrix} \right.} & (2)\end{matrix}$

That is, when the frequency distribution of the binary-coded image thathas the one gray level value x displays a high-pass filter-typefrequency distribution having a large response at the principalfrequency ƒ_(p), the image exhibits the ideal blue noise characteristic.

Equation 3 is an evaluation function defined by the above blue noisecharacteristic:

$\begin{matrix}{R = \frac{\sum\limits_{m}{\left( {A_{m} - \overset{\_}{A}} \right)\left( {B_{m} - \overset{\_}{B}} \right)}}{\sqrt{\left( {\sum\limits_{m}\left( {A_{m} - \overset{\_}{A}} \right)^{2}} \right)\left( {\sum\limits_{m}\left( {B_{m} - \overset{\_}{B}} \right)^{2}} \right)}}} & (3)\end{matrix}$Here, R represents the evaluation function, Ā represents an averageenergy in the optimal energy spectrum, A_(m) represents energy at eachfrequency in the optimal energy spectrum. B represents an average energyin a predetermined comparison energy spectrum, and B_(m) representsenergy at each frequency in the predetermined comparison energyspectrum.

The evaluation function, which ranges from −1 to 1, is determined bycomparing the comparison energy spectrum of each of N images to theoptimal energy spectrum, and thus N evaluation functions can be obtainedfor the N images.

The fit values are determined by adding together an evaluation functionin a low frequency region and an evaluation function in a high frequencyregion. The following Equation 4 is used to calculate the fit values:F _(k) =R _(k1) +R _(k2)  (4)Here, F_(k) represents the fit value, R_(k1) represents the evaluationfunction when f_(r)≦(f_(p)+α), and R_(k2) represents the evaluationfunction when f_(r)>(f_(p)+α). Equation 4 is the sum of evaluationfunctions for low and high frequency regions after dividing one energyspectrum into the low and high frequency regions.

Since the evaluation function ranges from −1 through 1, the fit value ofEquation 4 has a range of −2 through 2. The greater the fit value, themore similar the comparison energy spectrum to the optimal energyspectrum. That is, when the fit value is close to 2, the image qualityof the binary-coded image is good. N fit values of the N binary-codedimages are determined using Equation 4.

After step 14, it is determined that the detected number of the fitvalues is the predetermined value (step 16). For example, if thepredetermined value is 200, it is determined that the detected number ofthe fit values is 200 so that reproducing, substituting, and changingoperations, which will be described later, are repeated hundreds oftimes. If the predetermined number of fit values are all determined, thedetermination process is suspended.

After step 16, if it is determined that the N fit values are notdetected the predetermined times, the N groups of error diffusioncoefficients are reproduced according to a reproduction rate that isdetermined by the N fit values (step 18). If it is assumed that the sumof the rates of detecting each of N fit values is 1, the rate ofdetecting each fit value can be obtained using Equation 5:

$\begin{matrix}{P_{k} = \frac{F_{k}}{\sum\limits_{i = 1}^{N}F_{i}}} & (5)\end{matrix}$Here, P_(k) represents the reproduction rate with respect to a k^(th)fit value F_(k).

According to Equation 5, a rate of a predetermined fit value can becalculated from the sum of N fit values, and thus the reproduction rateof the predetermined fit value can be determined.

The N groups of error diffusion coefficients are reproduced according tothe reproduction rates of the fit values calculated using Equation 5.Since the quality of the binary-coded image is good when the fit valueis large, as many as possible error diffusion coefficients forbinary-coded images having large fit values are reproduced. Therefore,the N groups of error diffusion coefficients are reorganized as N newgroups of error diffusion coefficients, by which the quality of thebinary-coded image can be improved.

After step 18, some error diffusion coefficients are selected from amongthe reproduced N groups of error diffusion coefficients, and someportions of the data of the selected error diffusion coefficients areswitched with portions of error diffusion coefficients of another group(step 20). FIG. 7 illustrates an example of switching part of the dataof two error diffusion coefficients. Within the hatched box, binary dataof first and second error diffusion coefficients are switched. Inalternative embodiments, such data switching can be performed betweenerror diffusion coefficients of three or more groups.

After step 20, some error diffusion coefficients are selected from amongthe N groups of error diffusion coefficients that have portions of datathat were switched in step 20, and portions of the selected errordiffusion coefficients are changed (step 22). FIG. 8 illustrates anexample in which a part of the data of an error diffusion coefficient ischanged. Specifically, FIG. 8 shows a “1” changed into a “0”. Inalternative embodiments, two or more bits of binary data can be changed,and binary data of error diffusion coefficients belonging to two or moregroups can be changed.

After step 22, the N groups of changed error diffusion coefficients areregarded as new error diffusion coefficients, and the process goes tostep 12 (step 24). The error diffusion coefficients that have switchedand changed data from previous processes are determined as the new errordiffusion coefficients of the N groups. The new error diffusioncoefficients are used to binarize the image having a gray level value instep 12.

The N groups of error diffusion coefficients determined through theabove reproducing, switching, and changing processes result in higherfit values, by repeating the processes. Thus, the new error diffusioncoefficients are determined to be ideal error diffusion coefficients.

FIG. 9 illustrates energy spectra for a binary-coded image having a graylevel value of 195, FIG. 10 illustrates energy spectra of a binary-codedimage having a gray level value of 225, and FIG. 11 illustrates energyspectra of a binary-coded image having gray level value 250. Morespecifically, FIGS. 9( a), 10(a), and 11(a) illustrate optimal energyspectrums, and FIGS. 9( b), 10(b), and 11(b) illustrate comparisonenergy spectrums. As can be seen, the comparison energy spectrums ofimages that are binary-coded using error diffusion coefficientsdetermined through hundreds of repeated processes according to anembodiment of the present invention are similar to their respectiveoptimal energy spectrums. When the comparison energy spectrum is similarto the optimal energy spectrum, the quality of the image is good.

Hereinafter, an apparatus for determining error diffusion coefficientsaccording to an embodiment of the present invention will be describedwith reference to the accompanying drawings.

FIG. 12 is a block diagram illustrating an apparatus for determiningerror diffusion coefficients according to an embodiment of the presentinvention. The apparatus includes a coefficient setting unit 100, animage binarizing unit 110, a fit value detector 120, a detection numberchecking unit 130, a coefficient reproducing unit 140, a coefficientsubstituting unit 150, a coefficient changing unit 160, and acoefficient determining unit 170.

The coefficient setting unit 100 sets N groups of error diffusioncoefficients. The coefficient setting unit 100 sets the error diffusioncoefficients in response to a signal requesting a coefficient settingoperation, input through an input terminal IN1, and outputs the setresults to the image binarizing unit 110.

FIG. 13 is a block diagram illustrating an example 100A of thecoefficient setting unit 100 shown in FIG. 12. The coefficient settingunit 100A includes a coefficient generator 200 and a decoder 220.

The coefficient generator 200 generates the N groups of binary errordiffusion coefficients in response to a signal requesting a coefficientsetting operation, which is input through an input terminal IN2, andoutputs the generated results to the decoder 220. FIG. 4 shows anexample of the N groups of error diffusion coefficients generated by thecoefficient generator 200.

The decoder 220 decodes the N groups of binary error diffusioncoefficients into N groups of decimal error diffusion coefficients. Thedecoder 220 receives the N groups of error diffusion coefficientsgenerated by the coefficient generator 200, decodes them into decimalerror diffusion coefficients, and outputs the decoded results through anoutput terminal OUT1. FIG. 5 shows an example of the N groups of errordiffusion coefficients decoded by the decoder 220.

The image binarizing unit 110 binarizes an image having a single graylevel value using each of the error diffusion coefficients. The imagebinarizing unit 110 receives the N groups of error diffusioncoefficients, which are set in the coefficient setting unit 100,binarizes the image having one gray level value using the input errordiffusion coefficients, and outputs the binary-coded images to the fitvalue detector 120. Also, the image binarizing unit 110 receives the Ngroups of error diffusion coefficients, which are newly determined bythe coefficient determining unit 170, binarizes the image having onegray level value using the new error diffusion coefficients, and outputsthe binary-coded images to the fit value detector 120.

The fit value detector 120 determines N fit values using the evaluationfunction for each of the N binary-coded images input from the imagebinarizing unit 110, and outputs the results of the determinations tothe detection number checking unit 130. Here, information output to thedetection number checking unit 130 includes the detection number of theN fit values.

The fit value detector 120 detects the fit values of the N binary-codedimages by adding the evaluation function in a low frequency region andthe evaluation function in a high frequency region, using the relationbetween the optimal energy spectrum having a blue noise characteristicand the comparison energy spectrum that is compared to the optimalenergy spectrum as the evaluation function. The fit value detector 120preferably uses Equation 3 as the evaluation function, and detects thefit values for the binary-coded images using Equation 4.

The detection number checking unit 130 checks whether the N fit valuesare detected a predetermined number of times. For example, if thepredetermined number is 200, the detection number checking unit 130checks whether the fit values are detected 200 times. The detectionnumber checking unit 130 receives the information about the detectionnumber of the N fit values, which are detected by the fit value detector120, checks whether the fit values are detected a predetermined numberof times, and outputs the check results to the coefficient reproducingunit 140.

The coefficient reproducing unit 140 reproduces the error diffusioncoefficients according to the reproduction rates determined by thedetected N fit values. The coefficient reproducing unit 140 preferablydetermines the reproduction rates of the error diffusion coefficientsusing Equation 5. The coefficient reproducing unit 140 receives thecheck result that the number of detected fit values does not coincidewith the predetermined number from the detection number checking unit130, reproduces the N groups of error diffusion coefficients accordingto the reproduction rates determined by the detected N fit values, andoutputs the result to the coefficient substituting unit 150.

The coefficient substituting unit 150 selects optional error diffusioncoefficients in the reproduced N groups of error diffusion coefficients,and substitutes some portions of the binary data of selected errordiffusion coefficients with each other, and outputs the results to thecoefficient changing unit 160. FIG. 7 illustrates an example ofsubstituting portions of the data of error diffusion coefficients in twogroups.

The coefficient changing unit 160 selects error diffusion coefficientsin the N groups of error diffusion coefficients, some of which containsubstituted data, and changes portions of the data of the selected errordiffusion coefficients. The coefficient changing unit 160 receives the Ngroups of error diffusion coefficients including coefficients withportions of data that has been substituted, from the coefficientsubstituting unit 150, and selects error diffusion coefficients amongthe received N groups. The coefficient changing unit 160 then changesparts of the binary data in the selected error diffusion coefficients.FIG. 8 illustrates an example of some data in a selected error diffusioncoefficient being changed by the coefficient changing unit 160.

The coefficient determining unit 170 determines the N groups of errordiffusion coefficients including the changed error diffusioncoefficients as new error diffusion coefficients, and outputs the resultto the image binarizing unit 110. The coefficient determining unit 170receives the N groups of error diffusion coefficients including theerror diffusion coefficients that are changed by the coefficientchanging unit 160, and determines the changed error diffusioncoefficients as new error diffusion coefficients. The coefficientdetermining unit 170 outputs the new error diffusion coefficients to theimage binarizing unit 110 to binarize the image having one gray levelvalue using the newly determined error diffusion coefficients.

As described above, according to an exemplary apparatus and method ofdetermining error diffusion coefficients of the present invention, errordiffusion coefficients are determined using a propagation algorithm, anddesired error diffusion coefficients with respect to any input graylevel can be determined without resorting to trial and error. Inaddition, the evaluation function considering the blue noisecharacteristic is used to prevent generation of a pattern that isvisually unpleasant and to obtain an even distribution of the pattern.

While the present invention has been particularly shown and describedwith reference to exemplary embodiments thereof, it will be understoodby those of ordinary skill in the art that various changes in form anddetails may be made therein without departing from the spirit and scopeof the present invention as defined by the following claims and theirequivalents.

1. A method of determining error diffusion coefficients, which is usedin a printer that binarizes and prints an image, the method comprising:(a) setting a positive integer N groups of error diffusion coefficients,in which each group includes a plurality of coefficients; (b) binarizingan image having one gray level value using each of the N groups of errordiffusion coefficients; (c) detecting N fit values with respect to Nbinary-coded images using an evaluation function; (d) determiningwhether the fit values are detected a predetermined number of times; (e)when a detection number of the fit values does not coincide with thepredetermined number of times, reproducing the N groups of errordiffusion coefficients according to reproduction rates determined by theN fit values; (f) selecting optional error diffusion coefficients in thereproduced N groups of error diffusion coefficients, and substitutingportions of data of selected error diffusion coefficients with eachother; and (g) determining the N groups of error diffusion coefficientsincluding the error diffusion coefficients containing substituted dataas new error diffusion coefficients, and returning to step (b).
 2. Themethod of claim 1, wherein step (a) comprises: generating N groups ofbinary error diffusion coefficients; decoding the generated N groups ofbinary error diffusion coefficients into N groups of decimal errordiffusion coefficients.
 3. The method of claim 1, further comprising:selecting error diffusion coefficients among the N groups ofcoefficients including the error diffusion coefficients containingsubstituted data, and changing portions of the data of the selectederror diffusion coefficients.
 4. A method of determining error diffusioncoefficients, which is used in a printer that binarizes and prints animage, the method comprising: (a) setting a positive integer N groups oferror diffusion coefficients, in which each group includes a pluralityof coefficients: (b) binarizing an image having one gray level valueusing each of the N groups of error diffusion coefficients; (c)detecting N fit values with respect to N binary-coded images using anevaluation function; (d) determining whether the fit values are detecteda predetermined number of times; (e) when a detection number of the fitvalues does not coincide with the predetermined number of times.reproducing the N groups of error diffusion coefficients according toreproduction rates determined by the N fit values; (f) selectingoptional error diffusion coefficients in the reproduced N groups oferror diffusion coefficients, and substituting portions of data ofselected error diffusion coefficients with each other; and (g)determining the N groups of error diffusion coefficients including theerror diffusion coefficients containing substituted data as new errordiffusion coefficients, and returning to step (b); wherein step (c) usesa correlation coefficient between an optimal energy spectrum having anideal blue noise characteristic and a comparison energy spectrum of eachof the N binary-coded images, as the evaluation function.
 5. The methodof claim 4, wherein step (c) uses the following equation as theevaluation function:${R = \frac{\sum\limits_{m}{\left( {A_{m} - \overset{\_}{A}} \right)\left( {B_{m} - \overset{\_}{B}} \right)}}{\sqrt{\left( {\sum\limits_{m}\left( {A_{m} - \overset{\_}{A}} \right)^{2}} \right)\left( {\sum\limits_{m}\left( {B_{m} - \overset{\_}{B}} \right)^{2}} \right)}}},$wherein R represents the evaluation function, Ā represents an averageenergy in the optimal energy spectrum, A_(m) represents energy at eachfrequency in the optimal energy spectrum, B represents an average energyin the comparison energy spectrum, and B_(m) represents energy at eachfrequency in the comparison energy spectrum.
 6. The method of claim 5,wherein in step (c), the fit values of the binary-coded N images aredetected by adding the evaluation function in a low frequency region andthe evaluation function in a high frequency region.
 7. An apparatus fordetermining error diffusion coefficients, which is used in a printerthat binarizes and prints an image, the apparatus comprising: acoefficient setting unit that sets a positive integer N groups of errordiffusion coefficients, each group including a plurality ofcoefficients; an image binarizing unit that binarizes an image havingone gray level value using each of the N groups of error diffusioncoefficients; a fit value detector that detects N fit values withrespect to each of the N binary-coded images using an evaluationfunction; a detection number checking unit that checks whether the fitvalues are detected for a predetermined number of times; a coefficientreproducing unit that reproduces the N groups of error diffusioncoefficients according to reproduction rates determined by the detectedN fit values; a coefficient substituting unit that selects optionalerror diffusion coefficients in the reproduced N groups of errordiffusion coefficients, and substitutes portions of data of selectederror diffusion coefficients; and a coefficient determining unit thatdetermines the N groups of error diffusion coefficients including thesubstituted error diffusion coefficients as new error diffusioncoefficients, and outputs the result of the determination to the imagebinarizing unit.
 8. The apparatus of claim 7, wherein the coefficientsetting unit comprises: a coefficient generator that generates the Ngroups of binary error diffusion coefficients; and a decoder thatdecodes the generated N groups of binary error diffusion coefficientsinto N groups of decimal error diffusion coefficients.
 9. The apparatusof claim 7, further comprising: a coefficient changing unit that selectserror diffusion coefficients among the N groups of coefficientsincluding the error diffusion coefficients containing substituted data,and changes portions of the data of the selected error diffusioncoefficients.
 10. An apparatus for determining error diffusioncoefficients, which is used in a printer that binarizes and prints animage, the apparatus comprising: a coefficient setting unit that sets apositive integer N groups of error diffusion coefficients, each groupincluding a plurality of coefficients; an image binarizing unit thatbinarizes an image having one gray level value using each of the Ngroups of error diffusion coefficients; a fit value detector thatdetects N fit values with respect to each of the N binary-coded imagesusing an evaluation function; a detection number checking unit thatchecks whether the fit values are detected for a predetermined number oftimes; a coefficient reproducing unit that reproduces the N groups oferror diffusion coefficients according to reproduction rates determinedby the detected N fit values; a coefficient substituting unit thatselects optional error diffusion coefficients in the reproduced N groupsof error diffusion coefficients, and substitutes portions of data ofselected error diffusion coefficients; and a coefficient determiningunit that determines the N groups of error diffusion coefficientsincluding the substituted error diffusion coefficients as new errordiffusion coefficients, and outputs the result of the determination tothe image binarizing unit; wherein the fit value detector detects thefit values of the N binary-coded images by adding the evaluationfunction in a low frequency region and the evaluation function in a highfrequency region using a correlation coefficient between an optimalenergy spectrum having ideal blue noise characteristics and a comparisonenergy spectrum of each of the N binary-coded images, as the evaluationfunction.
 11. The apparatus of claim 10, wherein the fit value detectoruses the following equation as the evaluation function:${R = \frac{\sum\limits_{m}{\left( {A_{m} - \overset{\_}{A}} \right)\left( {B_{m} - \overset{\_}{B}} \right)}}{\sqrt{\left( {\sum\limits_{m}\left( {A_{m} - \overset{\_}{A}} \right)^{2}} \right)\left( {\sum\limits_{m}\left( {B_{m} - \overset{\_}{B}} \right)^{2}} \right)}}},$wherein, R represents the evaluation function, Ā represents an averageenergy in the optimal energy spectrum, A_(m) represents energy at eachfrequency in the optimal energy spectrum, B represents an average energyin the comparison energy spectrum, and B_(m) represents energy at eachfrequency in the comparison energy spectrum.